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bernouilli5.ae
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This is meant to be an extension of AAL's program for computing what
she called the fourth Bernouilli number B9 (what Wikipedia would call
B10).
I've scaled by 10 places where real arithmetic is implied
(i.e. dividends are shifted up 10 digits unless already scaled,
products are shifted down by 10 digits if both multiplicands are
scaled). Divide the result by 10**10 to get B9.
A bug in operation 4 has been fixed (the comment requires V4/V5,
AAL's code does V5/V4).
Another bug was at operation 24: the value accumulated in V13 is *the
negative* of the required value, see Note G Equation 9.
useful constants
n001 1
n002 2
which bernouilli number is required?
n003 5
b0 = 1
b1 = 0.1666666666
n021 01666666667
b3 = -0.0333333333
n022 -00333333333
b5 = 0.0238095238
n023 00238095238
b7 = -0.0333333333
n024 -00333333333
b9 = 0.0757575758 (expected!)
operation 1
*
l002
l003
s004
s005
s006
operation 2
-
z004
l001
s004
operation 3
+
z005
l001
s005
operation 4, with bug fixed
/
z004
<10
z005
s011'
operation 5
/
z011
l002
s011'
operation 6
-
z013
z011
s013
operation 7
l003
l001
s010
--------------------
operation 8
+
l002
l007
s007
operation 9
/
l006
<10
l007
s011'
operation 10, using b1 (v021)
*
l021
l011
>10
s012
operation 11
+
z012
z013
s013
operation 12
-
z010
l001
s010
--------------------
operation 13
-
z006
l001
s006
operation 14
+
l001
z007
s007
operation 15
/
l006
<10
l007
s008'
operation 16
*
z008
z011
>10
s011
operation 17
-
z006
l001
s006
operation 18
+
l001
z007
s007
operation 19
/
l006
<10
l007
s009'
operation 20
*
z009
z011
>10
s011
operation 21, using b3 (v022)
*
l022
l011
>10
s012
operation 22
+
z012
z013
s013
operation 23
-
z010
l001
s010
.................... first repeat starts here
operation 13
-
z006
l001
s006
operation 14
+
l001
z007
s007
operation 15
/
l006
<10
l007
s008'
operation 16
*
z008
z011
>10
s011
operation 17
-
z006
l001
s006
operation 18
+
l001
z007
s007
operation 19
/
l006
<10
l007
s009'
operation 20
*
z009
z011
>10
s011
operation 21 (NB using b5, v023 this time)
*
l023
l011
>10
s012
operation 22
+
z012
z013
s013
operation 23
-
z010
l001
s010
.................... second repeat starts here
operation 13
-
z006
l001
s006
operation 14
+
l001
z007
s007
operation 15
/
l006
<10
l007
s008'
operation 16
*
z008
z011
>10
s011
operation 17
-
z006
l001
s006
operation 18
+
l001
z007
s007
operation 19
/
l006
<10
l007
s009'
operation 20
*
z009
z011
>10
s011
operation 21 (NB using b7, v024 this time)
*
l024
l011
>10
s012
operation 22
+
z012
z013
s013
operation 23
-
z010
l001
s010
--------------------
operation 24, with bug fixed
-
z025
l013
s025
the result!!
p
operation 25
+
l001
z003
s003
-- and clear V6, V7 - why?
n006 0
n007 0